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Length of maximal prime gap p_{k+1} - p_k with starting prime p_k < 10^n.
4

%I #13 Feb 16 2025 08:32:42

%S 4,8,20,36,72,114,154,220,282,354,464,540,674,804,906,1132

%N Length of maximal prime gap p_{k+1} - p_k with starting prime p_k < 10^n.

%C Prime gaps associated with A053302.

%C a(17) is probably 1220 and a(19) is probably 1296. - _Robert G. Wilson v_, Mar 16 2004

%H Thomas R. Nicely, <a href="https://faculty.lynchburg.edu/~nicely/gaps/gaplist.html">First occurrence prime gaps</a> [For local copy see A000101]

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeGaps.html">Prime Gaps</a>

%e a(1) = 4 from 7 to 11. a(2) = 8 from 89 to 97. a(3) = 20 from 887 to 907.

%e a(5)=72 because the 5-digit prime 31397 begins a gap of 72.

%Y p_k's are in A053302. Cf. A005250, A002386. Essentially the same as A038460.

%K nonn

%O 1,1

%A _Enoch Haga_, Mar 05 2000

%E a(16) from _Eric W. Weisstein_, Mar 05 2004